Choosing among technologies is difficult and requires a means of making comparisons across different technologies. This dissertation proposes a new methodology to make comparisons across different technologies and across different times based on a user supplied set of evaluation criteria. A simple model is developed to evaluate different technologies and to identify optimal technologies and technology pathways based on a user supplied set of evaluation criteria which allow ranking of different plants, and technology pathways, which represent different time sequences of introducing new power plant designs. This model is applied to a simple set of choices for power plant designs that invovle eight basic operation modules and a total of 96 possible power plant designs, of which 18 are physically feasible. The model also considers five unique pathways of transition over time from one type of power plant to another type. These pathways are ranked based on penalties assigned on the module level, plant level and pathway level. This dissertation studies two cases, where CO2 regulation does and does not take effect. The results show that a shorter path is favorable, and multiple changes at the same time is undesirable. The relative ranking of different pathways are different in the two cases. To find the optimal path among the entire space of solutions, we develop two combinatorial optimization algorithms. The objective function is defined as the minimum of penalties which are imposed for all deviations from an ideal or perfect system. The numerical problem of finding an optimum is solved by means of a branch-and-bound method, and a heuristic based on the label-correcting algorithm for solving the shortest-path problem. The proposed algorithms are applied to the practical examples of finding the optimal sequence of various power plant designs. The computational results show that the performance of the path-dependent shortest path algorithms depends on the structure of the problem. For average problems, the branch-and-bound algorithm is more efficient compared with the brute force search approach. In the worst case, the branch-and-bound algoirthm degenerates into the brute-force search approach. Both branch-and-bound and the brute-force search approach are exact methods. For average problems, the heuristic is more efficient than the branch-and-bound algorithm. The heuristic is not an exact method and there is no guarantee that it always finds the optimum. However, it can find a good result in a reasonable time. We use these algorithms to study technology pathways which consist of power plant designs with CO2 post-combustion capture technologies. We consider a small problem that consists of 6 designs and 14 levels of decisions, a medium problem consisting of 84 designs and 15 levels of decisions, and a big problem consisting of 492 designs and 15 decisions. We use the branch and bound algorithm for the small problem, and the heuristic for the medium and big problems. The results of small, medium and big problems show that, the best technology pathway, or the best sequence of technologies, does not agree with the sequence of best technologies of various times. By choosing a suboptimal design upfront, one can obtain a better technology pathway than the pathway with a sequence of best designs. We develop a flexible software tool that enables process modeling and optimization of complicated energy systems. The software tool models a plant in terms of basic operation modules and streams that connect the modules with material and energy flows. The software represents the beginning of new modling capability that is useful for studying individual energy systems. It introduces a new concept in comparison to traditional software tools by optimizing over entire technology pathway consisting of a time sequence of plant designs and technology choices.